Fuzzy ϑ –BFGS Update for Numerical Optimization

Saad Shaker Mahmood, Alan Jalal Abdulqader


In this paper, we develop a quasi-Newton method for unconstrained optimization problems with fuzzy functions. Also, we Propose  the -BFGS method to fuzzy optimization problems. The generalized Hukuhara differentiability for fuzzy functions is employed. By using a Hessian approximation, we resolve the high computational cost of finding the Hessian in Newton method for fuzzy optimization problems. We will find the solutions of a fuzzy optimization problem. Finally, some numerical results support this claim and also indicate that the -BFGS update may be competitive with the BFGS update in general


Unconstrained fuzzy optimization problems, Quasi-Newton methods, Superlinear convergence, generalized Hukuhara differentiability,

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